Problem: Rewrite the function by completing the square. $f(x)=x^{2}+20x-86$ $f(x)=(x+$
We want to complete $x^2{+20}x$ into a perfect square. To do that, we should add $\left(\dfrac{{+20}}{2}\right)^2={100}$ to it: $x^2{+20}x+{100}=(x+10)^2$ In order to keep the expression equivalent, we add and subtract ${100}$, not forgetting the expression's constant term, $-86$ : $\begin{aligned} f(x)&=x^2+20x-86 \\\\ &=x^2+20x+{100}-86-{100} \\\\ &=(x+10)^2-86-100 \\\\ &=(x+10)^2-186 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x + 10)^2 - 186$